Problem: The value of $\log_{10}{28471}$ is between the consecutive integers $a$ and $b$.  Find $a+b$.
Explanation: We can have $\log_{10}10000=4$ and $\log_{10}100000=5$.  Since $\log_{10}x$ increases as $x$ increases, we know that $\log_{10}10000<\log_{10}28471<\log_{10}100000$, meaning $4<\log_{10}28471<5$.  Thus, the desired sum is $4+5=\boxed{9}$.